Distribution Analysis: Distributional Modeling

How Do the Data Deviate from Normality?

A normal Q-Q plot appears as the upper left plot in FigureĀ 15.6. A Q-Q plot graphically indicates whether there is agreement between quantiles of the data and quantiles of a theoretical distribution. The Q-Q plot for the normal distribution shows several points to the left that are below the diagonal line. These points indicate that the data distribution has a longer left tail than would be expected from normally distributed data. The point to the right that is above the line might indicate an outlier in the data. Table 15.1 describes how to interpret common features of a Q-Q plot.

The goodness-of-fit table in the output document shows that the p-values for the goodness-of-fit tests are very small. The null hypothesis for the goodness-of-fit tests is that the data are from a specified theoretical distribution. The smaller the p-value, the stronger the evidence against the null hypothesis. The small p-values in this example indicate that the normal distribution is not an adequate model to describe these data.

Note: The pressure_outer_isobar variable contains 4,669 nonmissing values. For a sample of this size, the goodness-of-fit tests can detect small departures from normality, so it is not surprising that these tests reject the null hypothesis.